Alexis has 52 coins in her coin purse that are either quarters or nickels. she has a total of $8 in her coin purse. how many nickels does alexis have? how many quarters does she have?

Let x number of quarters, y number of nickels

x + y = 52 so x = 52 - y
0.25x + 0.05y = 8

replace x = 52 - y into 0.25x + 0.05y = 8

0.25x + 0.05y = 8
0.25(52 - y) + 0.05y = 8
13 - 0.25y + .05y = 8
-0.2y = 8 -13
-0.2y = -5
y = 25

x = 52 - y
x = 52 - 25 
x = 27

there are 27 quarters

double check

0.25x + 0.05y = 8
0.25(27) + 0.05(25) = 8
6.75 + 1.25 = 8

-2x + 7 = 7

subtract 7 from both sides.

-2x = 0

divide both sides by -2.

x = 0

the value of x is equal to 0.